Abstract: Aiming at the disadvantages of existing optimization methods on solving high-dimensional multi-objective optimization problem,the multi-objective solution was mapped into fuzzy set,and the relative entropy of fuzzy sets representing the similar degree between fuzzy sets were used to solve multi-objective optimization problem.A multi-objective optimization method based on relative entropy of fuzzy sets was presented,and the size of fuzzy relational entropy coefficient was used to measure similar degree between the fuzzy sets of Pareto solutions and the fuzzy set of ideal solution.The coefficient used as Particle Swarm Optimization (PSO) fitness was applied to guide algorithm evolution,therefore the multi-objective PSO based on relative entropy of fuzzy sets was established.Experiments showed that PSO based on relative entropy of fuzzy sets could solve high-dimensional multi-objective flow shop scheduling problem effectively.The optimization solution and performance indicators of the algorithm were better than PSO based on random weight.Especially in solving large-scale problems,the performance of PSO based on relative entropy of fuzzy sets was much better.

Key words: fuzzy sets, fuzzy relative entropy, multi-objective optimization, particle swarm optimization, flow shop

摘要： 针对现有优化方法在求解高维多目标问题上的弊端,将多目标解映射为模糊集,提出利用表征模糊集间关联相似程度的模糊关联熵方法解决多目标优化问题。建立基于模糊关联熵的多目标优化方法,以模糊关联熵系数的大小衡量Pareto解模糊集与理想解模糊集的相似程度,并以该系数作为粒子群优化算法适应度值引导算法进化,建立基于模糊关联熵的多目标粒子群优化算法。实验表明,基于模糊关联熵的粒子群优化算法可以有效解决高维多目标Flow Shop调度问题,算法在优化解和各性能指标上皆优于基于随机权重的粒子群优化算法,特别在求解较大规模问题时,基于此法的粒子群优化算法表现更佳。

关键词: 模糊集, 模糊关联熵, 多目标优化, 粒子群优化算法, 流水车间